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In this study we address the question of the minimum sample size needed for distinguishing between Gutenberg-Richter distributions with varying b-values at different resolutions. In order to account for both the complete and incomplete…

The district of southern California and Japan are divided into small cubic cells, each of which is regarded as a vertex of a graph if earthquakes occur therein. Two successive earthquakes define an edge and a loop, which replace the complex…

We study the distributions of earthquake numbers in two global catalogs: Global Centroid-Moment Tensor and Preliminary Determinations of Epicenters. These distributions are required to develop the number test for forecasts of future seismic…

We study the mixing time of random graphs in the $d$-dimensional toric unit cube $[0,1]^d$ generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a…

Extending the central concept of recurrence times for a point process to recurrent events in space-time allows us to characterize seismicity as a record breaking process using only spatiotemporal relations among events. Linking record…

This paper is devoted to reduce the conservatism of distributionally robust optimization with moments information. Since the optimal solution of distributionally robust optimization is required to be feasible for all uncertain distributions…

Crustal deformation due to the 2016 earthquake sequence in Kumamoto, Japan, that culminated in a preceding earthquake of magnitude M6.5 and a subsequent M7.3 earthquake 28 hours later, caused stress perturbation on and around the causative…

The gapped local alignment score of two random sequences follows a Gumbel distribution. If computers could estimate the parameters of the Gumbel distribution within one second, the use of arbitrary alignment scoring schemes could increase…

The measurement of the size of gravitationally bounded structures is an important test of gravity theories. For a given radius different theories can in fact predict a different gravitational stability mass (GSM) necessary to ensure the…

We introduce a new technique for bounding the cover time of random walks by relating it to the runtime of randomized broadcast. In particular, we strongly confirm for dense graphs the intuition of Chandra et al. \cite{CRRST97} that "the…

We present a new kind of critical stochastic finite-time-singularity, relying on the interplay between long-memory and extreme fluctuations. We illustrate it on the well-established epidemic-type aftershock (ETAS) model for aftershocks,…

In [Engquist et al., Commun. Math. Sci., 14(2016)], the Wasserstein metric was successfully introduced to the full waveform inversion. We apply this method to the earthquake location problem. For this problem, the seismic stations are far…

The upcoming direct detection of gravitational waves will open a window to probing the strong-field regime of general relativity (GR). As a consequence, waveforms that include the presence of deviations from GR have been developed (e.g. in…

In this paper, we introduce a new four-parameter generalized version of the Gompertz model which is called Beta-Gompertz (BG) distribution. It includes some well-known lifetime distributions such as beta-exponential and generalized Gompertz…

As an object of study, we chose the global activity of strong earthquakes (M > 7). The subject of the study is the waiting time for the next strong earthquake. The purpose of the study is to compare two distributions of waiting time, one of…

We estimate the possible variations of the gravitational constant G in the framework of a generalized (Bergmann-Wagoner-Nordtvedt) scalar-tensor theory of gravity on the basis of the field equations, without using their special solutions.…

We explore in depth the validity of a recently proposed scaling law for earthquake interevent time distributions in the case of the Southern California, using the waveform cross-correlation catalog of Shearer et al. Two statistical tests…

Let $\cT$ be Teichm\"uller space of a closed surface of genus at least 2. For any point $c\in \cT$, we describe an action of the circle on $\cT\times \cT$, which limits to the earthquake flow when one of the parameters goes to a measured…

We study random surfaces with a uniformly convex gradient interaction in the presence of quenched disorder taking the form of a random independent external field. Previous work on the model has focused on proving existence and uniqueness of…

We study statistical properties of the number of large earthquakes over the past century. We analyze the cumulative distribution of the number of earthquakes with magnitude larger than threshold M in time interval T, and quantify the…